Statistics for Business Decisions: An Analysis of Factors Affecting the Selling Price of Houses in the Australian Real Estate Industry

HM6007

Statistics for Business Decisions

Student Name:

Student ID:

Introduction

The report explores the Australian real estate industry in an effort to determine an outline and activities affecting the selling price of houses. In the study, the consideration given to the variables include the size of the land, number of bedrooms, the proximity of the house from the nearest second school and the number of spaces in the garage with regards to the price of the house. The data set used in this work includes data compiled from 100 residential properties sold after 1st April 2024. Descriptive, regression, and correlation analyses where employed in order to analyze the connection between these variables and the selling price.

Descriptive statistical Analysis

If any of these conditions prove true, then the use of descriptive statistics which offer an overview of the central tendencies, variability and distribution of each of the variables in the data sets feeds into this form of analysis function. The following variables were considered in the analysis (Warton, 2022).

Land Size (m²)

First, mean size of the lands in the dataset was 866.35 m sqr while its standard deviation was 1172.76 m sqr. This large value for the standard deviation is a sign of a great variation in the size of the properties it is likely that such a set contains small properties as well as large ones. The minimum required land size is one hundred square meters and the summarize is nine thousand one hundred square meters.

No. of KM to Secondary School

Geometrically, the mean distance to the nearest second school is 1.56 Kms with SD 3.08 Kms. These a broad range makes it clear that certain properties are near schools whereas others are far from schools.

Number of Garage Spaces

The mean for number of garage Spaces 2.53 and standard deviation of number of garage spaces is 1.53 which mean that despite the majority of properties having 2 garage spaces there are some which have more or less garage space.

Number of Bedrooms

The number of bedrooms is mean is 3.46 to 4.46 and standard deviation for bedrooms is 0.83. 67% of the houses in the dataset have 3 to 4 bedrooms with the mode having 3 bedrooms.

Selling Price ($)

The average selling price is $999,281 and the coefficients of variation is quite high @ $742,021. One can also understand why the houses cost from $105,000 to $5,100,000, as in reality, it characterized by the area, location and other parameters.

Graphical Representations

Two key graphical representations were used to visualize the data

Histogram of Bedrooms

Histogram of the number of bedrooms is also positively skewed, and most of the houses have 3 or 4 bedrooms. This means that three bedrooms home density is the highest in the dataset used.

Scatter Plot of size and price of land on sale

The first graph represents the sales price relative to size of the land. The correlation between the selling price and land size exists, whereas the plot illustrates an existence but weak linear relationship between the two variables does not support the hypothesis that the size of the land is sufficient to determine the selling price.

Multiple Regression Analysis

To understand the factors influencing the selling price, a multiple regression analysis was performed using the following independent variables, using the independent variables such as land size, distance to the nearest secondary school, number of bedroom, number of garage spaces.

Interpretation of coefficients

Intercept

The value of 420900 can be interpreted that the intercept means that the base price at which a property is sold when controls are set to zero is $420,900. Selling prices are then predicted from this value.

Land Size

If we take everything equal and add one square meter, the price at which land is sold increases by $8.31. They concluded that large quantities of property are more valuable, but units in square meter gains are relatively small.

Distance to School

The selling price rises by $10,747 for each extra kilometre that a property is from the nearest secondary school. This somewhat counter intuitive finding means that properties which are farther from schools are likely to cost more, which could be due to the fact that quiet neighbourhoods or high value homes might be situated away from school zones.

Garage Spaces

Finding an extra garage space raises the price by $ 9,789. This means that properties with higher number of garage spaces are more appreciated because in most cases people consider a garage as a necessary commodity at their backyards.

Coefficient of Determination (R²)

The R- squared value for this model is 0.034; therefore, explaining only 3.4% of variation in the selling prices of the houses from the independent variables; land size, distance to school and number of garage spaces. This low value of R-squared means that there are other characteristics that drive property prices and the model itself explains few of them.

Model Significance

The overall significance of the regression model was conducted using the F-test at 0.05 level of significance. The obtained p-value of 0.508 further puts into view that the model as a whole is statistically insignificant, in other words there is insufficient evidence to suggest that all the independent variables combined affect the selling price of the house. Hence the model to a certain extent, offers some measure of prediction accuracy of property prices bearing in mind the factors considered above (Brusco, 2022).

Significance independent variables

When predicting at it 5% level of significance, all the independent variables; land size, distance to school and garage spaces show statistically insignificant. This means that, when taken separately, these variables cannot predict the selling price as being much different from the other variables.

Correlation Analysis and Multicollinearity

In order to test the interrelationships amongst the independent variables, a correlation matrix was calculated for each of the independent variables; to check if multicollinearity was present. The analysis of the correlation matrix shown that there was low correlations among the variables and therefore there was no issues of multicollinearity. This goes further to support the assumption that independent variables are orthogonal; thus, each independent variable used is dependent on no other variable in the model.

Summary

The purpose of this study was to determine the impact that size of the land, number of bedrooms, distance to schools and number of garage spaces has on the price of the residential houses. Based on the multiple regression analysis, the following conclusions can be drawn.

• Such attributes as land size, distance to school and garage spaces are only slightly significant because they show low coefficients and R-square values that indicate low predictability.

• The R-squared of the model 0.034) means that the factors examined in this work account for a very small portion of the variation in selling prices. This implication can also point to the likelihood that characteristics of IDs such as neighbourhood, property condition and market forces perhaps have a stronger relation with the value of the residential properties.

• The overall model was not statistically significant, with the chi-square of 144.394 (p < 0.05) indicating that at least one independent variable is significant at the 5% level.

Conclusion

In Conclusion, based on the factors analysed in this paper, knowledge relating to the pricing of residential properties can only be Partial. More studies should take into analysis location of property, consumer preferences, and other characteristics that perhaps might affect real estate to a greater extent.

References

Brusco, M., 2022. Logistic regression via Excel spreadsheets: Mechanics, model selection, and relative predictor importance. INFORMS Transactions on Education, 23(1), pp.1-11. https://pubsonline.informs.org/doi/pdf/10.1287/ited.2021.0263

Eco-stats: Data analysis in ecology. Cham, Switzerland: Springer Nature Switzerland AG. https://link.springer.com/content/pdf/10.1007/978-3-030-88443-7.pdf